There are two obvious extremes to avoid. NPC-as-bazooka(note 2), and the ever dreaded Escort Mission, where the NPC is obviously helpless.
However, there is a far more fatal trap: Giving a bazooka to a Tier 1 character. The depressing thing is that at level 5, a wizard or cleric with access to all of the books will destroy a ECL 5 dragon. A Brass Dragon Wrymling, ECL 6, has pathetic saves, a pathetic breath weapon, and no spell resistance.
This is still better than a Tier 5 Fighter or arguably Tier 4 Rogue because of its breath weapon, and movement modes. I'd allow a Tier 5 or 4 to play the dragon without modifications if most of the party is averaging Tier 2. If you have a Tier 5 character in your party and the party is around tier 2, the simplest solution is to ask that player if they would like to play the dragon as well as their character.
If the group is around Tier 2, with everyone between 1-3, the easiest expedient would be for one PC to play the dragon voluntarily and abandon their current character. Unfortunately, for things that this level of group will find difficult, the dragon will be hopelessly overwhelmed and die quite easily. Not quite as easily as a normal familiar, but close...
Under no circumstances should you apply the buffs granted by the familiar features to the dragon on top of the dragon's inherent attributes. That's just cheesy. (But only very mild flavours of cheese. It's not like the character is casting Awaken Beast on herself for Nigh-Infinite Intelligence...)
If you give us more details about the group, I can narrow my answer down more.